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Solution assignment 27 Differentiation of standard functions

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Assignment 27

Differentiate:

y=\displaystyle\frac{8x^2+5x}{x^2}

Solution

This function is a quotient and we do not know yet how to differentiate a quotient (this will be explained in: Differentiation Product and Quotient rule).
When we take a closer look we notice that the function can be rewritten as:

y=\displaystyle\frac{8x^2}{x^2}+\displaystyle\frac{5x}{x^2}=8+\displaystyle\frac{5}{x}=8+5x^{-1}

The derivative of this function is not hard to find:

y'=0+5.-x^{-2}=-\displaystyle\frac{5}{x^2}

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